Solve 2D discrete time equation

Hellow, In linear algebra or image processing or the problem that we need solve the following discrete time equation in the case of two dimensional state space:

x(i+1,j+1)=A*x(i,j) ..............(*******) ,

such that the vector x(i,j) is a vector and A is a matrix for example we have the initial conditions are x(0,j) =0 and x(i,0)=0 for all values of i and j and A=[-8 7; 4 3]. ( numericcaly we suppose for example max of i and j = 10.

to plot the solution x(i,j) of the given equation (*******), I use the following code matlab:

clc, clear all,

A=[-8 7; 4 3];

for j=1:10

x{1,j}=0;

end

for i=1:10

x{i,1}=0;

end

for i=1:10

for j=1:10

x{i+1,j+1}=A*x{i,j}

end

end

is that corect ? and If not how we can make it ?? ( i and j are axis and x(i,j) the solution surf )

Answer 1

[Lewis Fr]

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